This idea is way out there and I have no idea if it would work, but could you drill say a 1/4” hole in the bottom of the stand to the stone and use a rod to apply pressure to the stone? Something like a 2-jaw gear puller might allow you to keep a little pressure on the stone while you heat it up.
View attachment 1494205
Are you... thinking outside the box???
Thank you, thank you. Yes - I’m here all week.